Online Conformal Inference with Retrospective Adjustment for Faster Adaptation to Distribution Shift

TL;DR

This paper introduces an online conformal inference method with retrospective adjustment that quickly adapts to changing data distributions by retroactively updating past predictions, improving coverage and efficiency.

Contribution

It proposes a novel online conformal inference technique with retrospective adjustment for faster adaptation to distribution shifts in streaming data.

Findings

Faster coverage recalibration demonstrated on synthetic data.

Improved statistical efficiency over existing methods.

Effective adaptation to real-world distribution changes.

Abstract

Conformal prediction has emerged as a powerful framework for constructing distribution-free prediction sets with guaranteed coverage assuming only the exchangeability assumption. However, this assumption is often violated in online environments where data distributions evolve over time. Several recent approaches have been proposed to address this limitation, but, typically, they slowly adapt to distribution shifts because they update predictions only in a forward manner, that is, they generate a prediction for a newly observed data point while previously computed predictions are not updated. In this paper, we propose a novel online conformal inference method with retrospective adjustment, which is designed to achieve faster adaptation to distributional shifts. Our method leverages regression approaches with efficient leave-one-out update formulas to retroactively adjust past predictions when new data arrive, thereby aligning the entire set of predictions with the most recent data distribution. Through extensive numerical studies performed on both synthetic and real-world data sets, we show that the proposed approach achieves faster coverage recalibration and improved statistical efficiency compared to existing online conformal prediction methods.